My question is whether Halmos' book "Naive Set Theory" is still up-to-date concerning contemporary mathematics; that is, is it outdated or not?
I really love the book so far, and while it's clear the notation is outdated, so far nothing contradicts what we had in the lectures. My assistant in calculus warned me about the book not being the newest though, so I'm a little confused right now.
Can I safely continue reading it without learning anything wrong or should I look for another book? If the latter is the case, can anyone of you give me a suggestion which book would be better suited?
Thanks in advance!
Sincerely, SDV
It's still an excellent book. You will certainly not learn anything wrong by reading it. The notation is quite the standard one and the approach is crystal clear and highly relevant. The only negative thing I have to say about the book is about its proof of Zorn's Lemma from the Axiom of Choice. It's technically quite involved to my taste, especially considering that there are other very elegant proofs. For instance, the proof given in "Sets, Models and Proofs" by Moerdijk and van Oosten, which is generally a good supplement to Halmos' Naive Set Theory.